基于复杂度追踪的模态参数识别方法对比研究  

Comparative study on modal parametric identification methods based on complexity pursuit

作　　者：胡志祥[1] 黄磊 郅伦海 胡峰 HU Zhixiang;HUANG Lei;ZHI Lunhai;HU Feng(College of Civil Engineering,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]合肥工业大学土木与水利工程学院,合肥230009

出　　处：《振动与冲击》2024年第15期22-31,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金面上项目(52178283);安徽省自然科学基金杰出青年基金(2108085J29)。

摘　　要：复杂度追踪(complexity pursuit, CP)是求解振动信号盲源分离(blind source separation, BSS)问题的一类经典方法。用复杂度追踪估计解混矩阵主要有基于源信号复杂度计算的梯度下降(complexity pursuit-gradient descent, CP-GD)算法和基于时间可预测度的广义特征值分解(temporal predictability-generalized eigenvalue decomposition, TP-GED)算法。当前,这两种算法的关联性与算法性能尚缺乏研究,因此对这两种算法的等价性和计算性能进行了研究。首先,给出CP-GD和TP-GED两种算法的具体理论及算法流程;其次,利用二、三自由度振动系统直观地展示并对比解混向量对应的源信号复杂度及可预测度的变化规律;最后,通过对多工况下多自由度系统的模态参数识别算例,对比研究两种算法的精度及计算量。研究结果表明:在低阻尼比及高信噪比条件下,两种方法得到的解混矩阵是相同的;考虑到计算信号复杂度和梯度下降较为耗时,CP-GD算法计算代价要高于TP-GED算法。Complexity pursuit(CP)is a classic method for solving blind source separation(BSS)problem of vibration signals.Two main methods for estimating a de-mixing matrix using complexity pursuit are the complexity pursuit-gradient descent(CP-GD)algorithm based on source signals complexity calculation and the temporal predictability-generalized eigenvalue decomposition(TP-GED)algorithm based on temporal predictability.Currently,there is a lack of study on the correlation and performance of these two algorithms.Here,the equivalence and computational performance of these two algorithms were studied.Firstly,the specific theories and algorithm procedures of CP-GD and TP-GED algorithms were presented.Secondly,using 2-degree-of-freedom and 3-degree-of-freedom vibration systems,changes of source signal complexity and predictability corresponding to de-mixing vectors were intuitively demonstrated and compared.Finally,the accuracy and computational amount of the two algorithms were studied contrastively by using modal parametric identification examples of multi-DOF systems under multiple operating conditions.The study results showed that under low damping ratio and high signal-to-noise ratio conditions,the two methods obtain the same de-mixing matrix;considering calculating signal complexity and gradient descent is more time-consuming,CP-GD algorithm has a higher computational cost than TP-GED algorithm does.

关 键 词：盲源分离(BSS) 模态参数识别 柯尔莫哥洛夫复杂度 时间可预测度(TP) 梯度下降(GD) 广义特征值分解(GED) 

分 类 号：TB123[理学—工程力学] TN911.6[理学—力学]